(3x+2)(4x-5)=0

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Solution for (3x+2)(4x-5)=0 equation: 


Simplifying
(3x + 2)(4x + -5) = 0

Reorder the terms:
(2 + 3x)(4x + -5) = 0

Reorder the terms:
(2 + 3x)(-5 + 4x) = 0

Multiply (2 + 3x) * (-5 + 4x)
(2(-5 + 4x) + 3x * (-5 + 4x)) = 0
((-5 * 2 + 4x * 2) + 3x * (-5 + 4x)) = 0
((-10 + 8x) + 3x * (-5 + 4x)) = 0
(-10 + 8x + (-5 * 3x + 4x * 3x)) = 0
(-10 + 8x + (-15x + 12x2)) = 0

Combine like terms: 8x + -15x = -7x
(-10 + -7x + 12x2) = 0

Solving
-10 + -7x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -3x)(5 + -4x) = 0


Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-0.6666666667, 1.25}

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